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Part $1$

Miami Mining Company $($Upper M$$MC$)$ mines$$ coal, puts it through a$$ one$-$step crushing$$ process, and loads the bulk raw coal onto river barges for shipment to customers. Upper M$$MC$\text{'}$s management is currently evaluating the possibility of further processing the raw coal by sizing and cleaning it and selling it to an expanded set of customers at higher prices. The option of building a new sizing and cleaning plant is ruled out as being financially infeasible.$$ Instead, Amy$$ Kimbell, a mining$$ engineer, is asked to explore$$ outside$-$contracting arrangements for the cleaning and sizing process. Kimbell puts together the following$$ summary:

Data table

$\backslash$table$[[,$A$,$B$,$C$],[1,$Selling price of raw coal,$$26$ per ton,$],[2,$Cost of producing raw coal,$$18$ per ton,$],[3,$Selling price of sized and cleaned coal,$$34$ per ton,$],[4,$Annual raw coal output,$10,000,000$ tons,$],[5,$Percentage of material weight loss in sizing$/$cleaning coal,$8\%,],[6,,\backslash$table$[[$Incremental Costs of Sizing$],[$& Cleaning Processes$]],],[7,$Direct labor,$$780,000$ per year,$],[8,$Supervisory personnel,$$200,000$ per year,$],[9,$Heavy equipment: rental, operating, maintenance costs,$$30,000$ per month,$],[10,$Contract sizing and cleaning,$$3\mathrm{.}60$ per ton of raw coal,$],[11,$Outbound rail freight,$$230$ per $600-$ton rail car,$],[12,\backslash$table$[[$Percentage of sizing$/$cleaning waste that can be salvaged for coal$],[$fines$]],75\%,],[13,$Range of costs per ton for preparing coal fine for sale,$$1,$$$16],[14,$Range of coal fine selling prices $($per ton$),$$$,]]$

More information: Kimbell also learns that$75\%$ of the material waste that occurs in the cleaning and sizing process can be salvaged as coal$$ fines, which can be sold to steel manufacturers for their furnaces. The sale of coal fines is erratic. The selling price of coal fines ranges from $ $16$ to $ $24$ per$$ ton, and costs of preparing coal fines for sale range from $ $1$ to $ $5$ per ton.

Requirements:

$1.$

Prepare an analysis to show whether it is more profitable for Upper MMC to continue selling raw bulk coal or to process it further through sizing and cleaning.$($Ignore coal fines in your$$ analysis.$)$

$2.$

How would your analysis be affected if the cost of producing raw coal could be held down to $ $16$ per$$ ton?

$3.$

Now consider the potential value of the coal fines and prepare an addendum that shows how their value affects the results of your analysis prepared in requirement $1.$